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39. Let (J,≤) be the partially ordered set with J = {0,1} and with 0 < 1. By identifying the subsets of a set X of n elements with the n-tuples of Os and 1s, prove that the partially ordered set (X, C) can be identified with the n-fold direct product (J,≤) × (J,≤) × x (J,≤) (n factors).

39. Let (J,≤) be the partially ordered set with J = {0,1} and with 0 < 1. By identifying the subsets of a set X of n elements with the n-tuples of Os and 1s, prove that the partially ordered set (X, C) can be identified with the n-fold direct product (J,≤) × (J,≤) × x (J,≤) (n factors).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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39. Let (J,≤) be the partially ordered set with J = {0, 1} and with 0 < 1. By identifying the subsets of a set X of n elements with the n-tuples of Os and 1s, prove that the partially ordered set (X, C) can be identified with the n-fold direct product (J,≤) × (J,≤) × x (J,≤) (n factors).
Transcribed Image Text:39. Let (J,≤) be the partially ordered set with J = {0, 1} and with 0 < 1. By identifying the subsets of a set X of n elements with the n-tuples of Os and 1s, prove that the partially ordered set (X, C) can be identified with the n-fold direct product (J,≤) × (J,≤) × x (J,≤) (n factors).
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